(CBS News) It's "wonderful" that lawmakers from both parties are working together on immigration reform, Arizona Gov. Jan Brewer said today on "Face the Nation." But for a congressional body 3,000 miles away from her state's border with Mexico to dictate that more secure borders are not a necessary prerequisite, she continued, is "wrong."

"We need to secure our border first and then move forward - I feel very, very strongly about that," the GOP governor said. Thanking Sen. Marco Rubio, R-Fla. - the son of Cuban immigrants - for leading that argument on Capitol Hill, she predicted it's "going to be a stumbling block trying to get something done" on immigration.

Brewer - who in 2010 signed the Arizona immigration law that sparked nationwide controversy and which was largely struck down last year by the Supreme Court - said she's witnessed Mexican drug cartels camp along the border and cross at night. The border patrol, she said, "is too far north. They need to be closer to the line."

"Our fences aren't complete," Brewer continued. "People are living down there in fear of their lives, and fear of the safety of their families. And we are recipients of all the crime that is taking place-the extortion, the human trafficking, the prostitution, the cost in jails. It's a bad problem."

Appearing with Brewer, though, two Democratic governors said while beefing up border security is a priority, it has to be part of a comprehensive package - a path Brewer argued the government has been down before.

"I think we do need to provide better border security, but I think that also we need to accomplish comprehensive immigration reform," Gov. Martin O'Malley, D-Md., said. "It'll be a lot easier to secure the borders and also to provide the correct level of enforcement if we allow hard-working people who have lived their whole lives in the United States to pay their taxes and live in the full light of society and be citizens."

Gov. John Hickenlooper, D-Colo., said that while he doesn't have "as much of a problem doing the border security first," he agreed that "in the end, you've got to really focus on the whole problem at the same time, right?

"You've got to look at employment identification, and making sure that 20 years down the road we're not going to get back in the same position," he continued.

"That requires not just a secure border, but an employment verification system that's rigorous, and a willingness to, you know, stand up and say, alright, everybody plays by the same rules, and everyone hires, you know, people that are supposed to be hire-able."